Victor Hakim

Date of Award


Document Type



Santa Clara : Santa Clara University, 2021.

Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Mohammad Ayoubi


This thesis presents the problem of optimal steering with three or two single-gimbal control moment gyros (SGCMGs). Most SGCMG configurations use more than three rotors so that the resulting Jacobian always has a nontrivial nullspace. We consider the specific case of a four-CMG pyramid configuration where only three or two CMGs are operational. We use the Gauss pseudospectral method to find the optimal gimbal angle trajectories of the CMGs and the states of an agile spacecraft subject to mission-specific constraints. We do so while either minimizing time or maximally avoiding the angular-momentum singularities. The proposed steering method is implemented in scenarios where the gimbal angles initially start in both nonsingular and singular positions. A closed-loop quaternion feedback steering law is also developed to reduce total CMG angular momentum, which ensures solution existence in the case of two CMGs. Results are compared with the standard four-SGCMG maneuvering via the generalized singularity robust steering law in the literature.